jee-main 2021 Q64

jee-main · India · session3_20jul_shift1 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions

The coefficient of $x ^ { 256 }$ in the expansion of $( 1 - x ) ^ { 101 } \left( x ^ { 2 } + x + 1 \right) ^ { 100 }$ is:
(1) ${ } ^ { 100 } C _ { 16 }$
(2) ${ } ^ { 100 } C _ { 15 }$
(3) ${ } ^ { - 100 } C _ { 16 }$
(4) ${ } ^ { - 100 } C _ { 15 }$

The coefficient of $x ^ { 256 }$ in the expansion of $( 1 - x ) ^ { 101 } \left( x ^ { 2 } + x + 1 \right) ^ { 100 }$ is:\\
(1) ${ } ^ { 100 } C _ { 16 }$\\
(2) ${ } ^ { 100 } C _ { 15 }$\\
(3) ${ } ^ { - 100 } C _ { 16 }$\\
(4) ${ } ^ { - 100 } C _ { 15 }$

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